Coupled-cluster theory of a gas of strongly-interacting fermions in the dilute limit

Abstract

We study the ground-state properties of a dilute gas of strongly-interacting fermions in the framework of the coupled-cluster expansion (CCE). We demonstrate that properties such as universality, opening of a gap in the excitation spectrum and applicability of s-wave approximations appear naturally in the CCE approach. In the zero-density limit, we show that the ground-state energy density depends on only one parameter, which in turn may depend at most on the spatial dimensionality of the system.

Keywords:

• dilute fermion systems
• electron gas
• equation of state
• unitarity limit

Acknowledgements

Understanding how physical properties of condensed-matter systems come about as a function of system size and composition may represent the key for accomplishing the elusive goal of material design. Now, for the first time, it is possible to characterize, both experimentally and theoretically, the transition from individual atoms and molecules to the solid state 27. Jim Smith was one of the first to understand the far-reaching implications of such an effort for material discovery and design. Not only did he recognize the need for Super-Intense Neutral Beams of atomic clusters to facilitate the Analysis and Discovery (SINBAD) of new materials, but he also realizes that a predictive many-body theoretical component is critical for providing the linking across length scales, to improve the quantitative understanding of condensed-matter systems and contribute to the successful extrapolation of existing experimental data to regimes that are not accessible in the laboratory. Jim is particularly supportive of our approach based on the continuum coupled-cluster expansion 26 to study the many-body theory of strongly-interacting systems.

This work was supported by the Los Alamos National Laboratory under the auspices of the US Department of Energy, under the LDRD program at Los Alamos National Laboratory. The authors gratefully acknowledge useful conversations with P.B. Littlewood, J.L. Smith, J.F. Dawson and J.H. Heisenberg.